Differential equation

Brief Introduction

GCSE Mathematics is comprised of 6 strands; number, algebra, geometry and measures, statistics, ratio and rates of change, and probability. Our curriculum is designed to develop students’ problem solving skills from year 7 through to year 11 to meet the requirements of the new GCSE.

In Years 10 & 11, students predominantly in Set 1 will also work towards achieving a Level 2 Certificate in Further Mathematics. This course acts as a bridge between GCSE and A-Level mathematics, but is also particularly relevant for students wishing to study physics, engineering and computing (amongst other subjects) in further education.

 

maths 2

Areas of Study

  Autumn Spring Summer
Year 7 Standard Numbers and the number system

Calculating

Calculating: division

Visualising and constructing

Investigating properties of shapes

Algebraic proficiency: using formulae

 

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Measuring space

Investigating angles

Calculating fractions, decimals, and percentages

Solving equations and inequalities

Calculating space

Checking approximating and estimating

Mathematical movement

Presentation of data

Measuring data

Year 8 Standard / Year 7 Higher Numbers and the number system

Counting and comparing

Calculating

Visualising and constructing

Investigating properties of shapes

Algebraic proficiency: tinkering

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Measuring space

Investigating angles

Calculating fractions, decimals and percentages

Solving equations and inequalities

Calculating space

Checking approximating and estimating

Mathematical movement

Presentation of data

Measuring data

Year 9 Standard / Year 8 Higher

 

Number and the number system

Calculating

Visualising and constructing

Understanding risk 1

Algebraic proficiency: tinkering

Exploring fractions, decimals and percentages

Proportional reasoning

Pattern sniffing

Investigating angles

Calculating fractions, decimals and percentages

Solving equations and inequalities

Calculating space

Algebraic proficiency: visualising

Understanding risk 2

Presentation of data

Measuring data

Year 9 Higher Calculating

Visualising and constructing

Algebraic proficiency: tinkering

Pattern sniffing

Solving equations and inequalities 1

Calculating space

Conjecturing

Algebraic proficiency: visualising

Solving equations and inequalities 2

Understanding risk

Presentation of data

Year 10 Foundation Number 1: Lowest Common Multiple (LCM), Highest Common Factor (HCF), product of prime factors

Algebra 1: algebraic expressions including substitution, expansion and factorisation

Geometry and Measures 1: angles in parallel lines, bearing and polygons

Data Handling 1: averages and range

Number 2: decimals including estimation, upper and lower bounds

Geometry and Measures 2: 2D shapes – area and perimeter including parts of a circle (arc, sector, segment)

Algebra 2: solve equations including quadratics

Number 3: Fractions

Geometry and Measures 3: Transformation (including fraction scale factor), symmetry, similar shapes

Algebra 3: formulae including substitution, change of subject, distinguish equation / formula / expression / identity

Number 4: percentages including use of multiplier, compound interest

Data Handling 2: presenting data including pie chart, scatter diagram, frequency polygon, time series

Geometry and Measures 4: volume and surface area of 3D shapes including sphere and pyramids

Algebra 4: sequences including geometric, nth term of linear sequence

Number 5: ratio and proportion (direct and inverse)

Algebra 5: algebraic graphs – linear, quadratic, cubic and reciprocal

Geometry and Measures 5: measures including compound, conversion of measure, graphs

Algebra 6: inequalities – notation, on a line, and solving

Number 6: powers and roots including rules for indices and standard form

Geometry and Measures 6: Pythagoras’ theorem and trigonometry

Data Handling 3: probability

Geometry and Measures 7: constructions, loci and congruence

Algebra 7: solve simultaneous equations – algebraic and graphical methods

Algebra 8: vector geometry

Year 10 Higher Number 1: multiples, factors, primes, laws of indices (including fraction and negative), standard form, surds

Algebra 1: expressions – substitution, expansion, factorising, algebraic fractions

Geometry and Measures 1: angles in parallel lines, polygons, bearings, circle theorems

Data Handling 1: statistics including data collection / sampling, averages and range including grouped data, scatter diagrams, time series

Number 2: fractions and decimals including upper and lower bounds calculations

Geometry and Measures 2: 2D shapes – area and perimeter including parts of a circle (arc, sector, segment)

Algebra 2: linear equations and graphs including algebraic and graphical solutions of simultaneous equations

Number 3: percentages including use of multiplier (exponential growth and decay), reverse percentages

Geometry and Measures 3: Transformations including negative and fractional scale factor enlargement

Algebra 3: formulae and sequences – substitution and transpose formulae, nth term of linear and quadratic sequences

Geometry and Measures 4: trigonometry 1 including Pythagoras and 3D shapes

Data Handling 2: statistics 2 including cumulative frequency, box plots, and histograms

Geometry and Measures 5: 3D shapes – surface area and volume of prisms, pyramids, spheres, and the frustum

Algebra 4: algebraic graphs including quadratic, cubic, reciprocal, exponential

Number 4: ratio and proportion including direct and inverse proportion, and graphs

Geometry and Measures 6: Loci, construction and congruence

Algebra 5: inequalities including graphical solutions

 

Data Handling 3: probability

Algebra 6: further factorising quadratics including completing the square, manipulate and simplify algebraic fractions

Geometry and Measures 7: trigonometry 2 including sine and cosine rule, trigonometric graphs, area formulae

Algebra 7: solve quadratic equations including factorising, completing the square, formula, equations with fractions

Geometry and Measures 8: similar shapes including length, area and volume

Algebra 8: simultaneous equations – linear / quadratic equations, equation of circle, equation of tangent

Geometry and Measures 9: vectors in solve geometric problems

Algebra 9: transformation of functions including trigonometric graphs

 

Year 10 set 1 additional topics for FM Algebra

Solutions of linear equations

Geometry – perimeter and area of rectangles, triangles and circles, volume of solids

Algebraic and graphical solution of simultaneous equations in two unknowns (both linear or one linear and one quadratic)

Matrices

Coordinates

Index laws

Manipulation of surds

Year 11 Foundation Probability 1

Probability 2

Quadrilaterals and other polygons

Coordinates and graphs

Trial and improvement

Measurement 2

Quadratic graphs

Circles and cylinders

Pythagoras’ Theorem

Constructions and loci

Revision of topics identified in the mock

Revision of topics identified in the mock
Year 11 Middle Non-linear graphs

Constructions and loci

Trigonometry

Circle theorems

Revision of topics identified in the mock Revision of topics identified in the mock
Year 11 Higher Cumulative frequency

Probability

Circles, cylinders, cones, and spheres

Ratio and proportion

Measures and dimensions

Sequences and proof

Constructions and loci

Quadratic equations

Non-linear graphs

Circle theorems

Pythagoras Theorem and trigonometry

Further algebra

Transformation of graphs

Vectors

Further trigonometry

Year 11 Set 1 additional topics for FM Sequences Algebra – completing the square, solution of quadratic equations

Geometry – understand and use circle theorems

Pythagoras’ Theorem

The coordinate geometry of circles

Geometry – area of a triangle using ½absinC, sine and cosine rules in scalene triangles

Calculus – differentiation

Geometry – ratio of angles and their graphs

 

Assessment

Students will be assessed throughout all five academic years through the use of practise GCSE papers, end of unit assessments, fortnightly maths tracker tests, class work and homework.

Firefly/Extended Learning

Extended learning activities are set as according to the school policy, through the school’s virtual learning environment (VLE) Firefly. This way all tasks can be viewed by students and their parents/carers. We encourage daily use of Firefly with students regularly clearing completed tasks on the ‘Your Tasks’ section of their profile to maintain good organisation.

In addition to this Firefly also contains useful information and support material. Details about equipment, suitable calculators and assessment dates are kept up to date on the Mathematics pages. A range of practise examination papers, tutorial videos on different topics and a student moderated forum section are also available.

 

Exam Specifications

AQA GCSE Mathematics Specification

AQA GCSE Statistics Specification

AQA Level 2 Further Mathematics Specification

Online Resources

MyMaths – An online resource for all students to access for reference, practise and homework purposes. Students all have a personal login that enables them to keep a record of their progress across topics throughout their time at Trentham.

TTRockstars – TTRockstars (Times Table Rockstars) is an online system designed to support students in learning their times tables, vital for progress in a wide range of mathematic topics.

Mathswatch – A set of mathematics resources videos and worksheets.

Corbett Maths – Key Stage 4 online resource e.g. 5 a day GCSE 9-1, videos, worksheets etc

Justmaths

BBC Bitesize – Student resources for revising mathematics.

Apps

iMathematics – A tool for reference and practise purposes, particularly for number, algebra and geometry topics.

Minds of Modern Mathematics – An app that details practical applications and the historical developments made in the field of mathematics.

MyScript Calculator – A handwriting calculator particularly useful for developing understanding of the order of operations and mathematical syntax.

Calculator for iPad – A free calculator to make up for the absence of an existing one.

Geometry Pad – An app for creating interactive diagrams to assist in understanding a range of geometry topics.

Quick Graph – An app for plotting graphs from an equation.

Extra –curricular activities

  • Year 11 mock examination preparation (end of Autumn term)
  • Year 11 GCSE preparation (Summer term)
  • Maths support – Maths teachers welcome students to come and seek support
  • Chess club (weekly – see student briefing)